How do you simplify #(9sqrt2)/sqrt(6)#?

1 Answer
Ricardo A.
Jul 1, 2016

#3sqrt(3)#

Explanation:

First we recognize that #6=2*3#
That allows us to write #sqrt(6)# as #sqrt(2*3)#
Square roots of multiplications can be split so #sqrt(2*3)=sqrt(2)*sqrt(3)#
So,#(9sqrt(2))/(sqrt(2)*sqrt(3))#
That will allow us to eliminate the #sqrt(2)# from the top and bottom leaving us with #9/sqrt(3)#
Now we split 9 into #3*3# and further split one of those 3s into #sqrt(3)*sqrt(3)#
leaving: #(3*sqrt(3)*sqrt(3))/sqrt(3)#
Eliminate one of the #sqrt(3)# from the top and the one from the bottom leaving us with the final answer of:
#3sqrt(3)#

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